1. Field of the Invention
The present invention relates to a method of improving the quality of data obtained by well logging a borehole and, more particularly, to a method of detecting, locating and correcting impulse noise errors in log measurements using an inverse filtering technique which determines innovations in a measurement as part of the inverse filtering process. The innovations in a measurement is the new information contained therein not already contained in previous measurements.
2. Discussion of the Prior Art
Measurement of subsurface formation parameters by lowering a logging tool down a wellbore is routinely done to provide data for accurate evaluation of the formation. Among the parameters measured are electrical resistivity and conductivity, density, sonic travel time, natural radioactivity, and formation response to neutrons. At each point at which a measurement is made the distance along the wellbore from a reference datum to that point is recorded. A grouping, such as a display of the measured values as a function of depth, is known as the log of the measured formation parameter.
Numerous logging tools are used to obtain the various measurements, but there is a characteristic common to them all. That is, the tool does not in reality measure the desired parameter at a point in the formation adjacent to the point in the wellbore at which the measurement is made. What the tool actually measures is a weighted average of values of the parameter at points up and down the wellbore from the measurement point, as well as the value of the parameter at the measurement point.
One technique which has been used to sharpen the resolution of log values is inverse filtering, which processes the measured values to obtain better parameter estimates X.sub.j at each measurement point. One improved inverse filtering method using a recursive innovations technique is disclosed in co-pending U.S. patent application Ser. No. 577,093, filed Feb. 6, 1984, entitled "Method of Increasing the Vertical Resolution of Well Log Data", and assigned to the same assignee as the present invention. The entirety of the disclosure of this application is incorporated herein by reference.
Inverse filtering techniques can work well to improve log data resolution when there is little measurement noise present. However, such filters have not been found to work well with noisy data due to the fact that these filters amplify the noise and, in many cases, the amplified noise is the dominant component in the estimated value. Techniques that account for the measurement noise treat the inverse filtering problem as a problem in statistical estimation theory. Using this approach, the formation parameters to be estimated are treated as samples from a random process and characterized in terms of its first- and second-order statistical averages. Processing treatments are designed by minimizing some average function of the error between the estimated measurement value X.sub.j and the true measurement value X.sub.j. In doing this, the processing treatment becomes an estimator or procedure for determining an estimate of a sample from a random process (true parameter values), given samples from another random process (the measurements) that contain noise. The estimate produced by such an estimator balances the errors due to noise amplification and those due to incomplete sharpening in such a way that the total error between estimate and true value in minimized.
Noise correction and data sharpening techniques designed using estimation theory provide reliable and accurate measurement estimates so long as the noise obeys the statistical averages that are assumed. Representative of these techniques are those using the Kalman filter (see Bayless, J. W. and Brigham, E. O., "Application of the Kalman Filter to Continuous Signal Restoration", Geophysics, Vol. 35, No. 1, February 1970, pages 2-23); recursive innovations, as described in the above-referenced patent application Ser. No. 577,093, and Weiner filtering (see Foster, M. R., Hicks, W. G. and Nipper, J. T., "Optimum Inverse Filters Which Shorten the Spacing of Velocity Logs", Geophysics, Vol. 27, No. 3, June 1962, pages 317-326). Unfortunately, noise with characteristics significantly different from those assumed is frequently encountered. This type of noise is referred to as impulsive or spike noise and, when present, causes large errors in the measurements. Usually, the impulse noise occurs at isolated measurement points or, at most, extends over a few measurement points. Noise of this type is extremely difficult to characterize statistically in a way that would allow for a practical inverse filter design. The occurrence of such noise is unpredictable, and when it occurs its magnitude is equally unpredictable.
Since the impulse noise cannot easily be characterized in a statistical manner, it is difficult to account for its possible presence in the design of an inverse filter, and consequently such noise is difficult to remove from measured parameter values when employing an inverse filtering technique to sharpen data resolution.